Function reconstruct 

pub fn reconstruct(coeffs: &WaveletCoeffs) -> Result<Vec<f64>, FdarError>

Invert decompose: reconstruct the original signal from a coefficient pyramid.

Rebuilds the filter bank from coeffs.family, then folds the detail bands back in reverse level order (coarsest-first), calling [single_level_synthesis] with each level’s exact analysis-input length recovered from coeffs.level_lens. Returns exactly coeffs.signal_len samples. Never emits NaN/inf when inputs are finite.

Errors

• FdarError::InvalidDimension if the coefficient pyramid is internally inconsistent (band count / metadata mismatch).
• FdarError::InvalidParameter if the family is unsupported.